http://popups.lib.uliege.be/1373-5411/index.php?id=262 Publications of Auteurs Nicholas A. Nechval fr 0 http://popups.lib.uliege.be/1373-5411/index.php?id=3198 In this paper, a control theory is used for planning inspections in service of fatigue-sensitive aircraft structure components under crack propagation. One of the most important features of control theory is its great generality, enabling one to analyze diverse systems within one unified framework. A key idea, which has emerged from this study, is the necessity of viewing the process of planning in-service inspections as an adaptive control process. Adaptation means the ability of self-modification and self-adjustment in accordance with varying conditions of environment. The adaptive control of inspection planning process in service of fatigued aircraft structures differs from ordinary stochastic control of inspection planning process in that it attempts to reevaluate itself in the light of uncertainties in service of aircraft structures as they unfold and change. Thus, a catastrophic accident during flight can be avoided. Wed, 11 Sep 2024 17:02:22 +0200 Thu, 10 Oct 2024 16:27:31 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=3198 http://popups.lib.uliege.be/1373-5411/index.php?id=2836 For important fatigue-sensitive structures of aircraft whose breakdowns cause serious accidents, it is required to keep their reliability extremely high. In this paper, we discuss inspection strategies for such important structures against fatigue failure. The focus is on the case when there are fatigue-cracks unexpectedly detected in a fleet of aircraft within a warranty period (prior to the first inspection). The paper examines this case and proposes stochastic models for prediction of fatigue-crack growth to determine appropriate inspections intervals. We also do not assume known parameters of the underlying distributions, and the estimation of that is incorporated into the analysis and decision-making. Numerical example is provided to illustrate the procedure. Tue, 03 Sep 2024 15:00:02 +0200 Thu, 10 Oct 2024 16:16:27 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=2836 http://popups.lib.uliege.be/1373-5411/index.php?id=2741 Based on a random sample from the Weibull distribution with unknown shape and scale parameters, lower and upper prediction limits on a set of m future observations from the same distribution are constructed. The procedures, which arise from considering the distribution of future observations given the observed value of an ancillary statistic, do not require the construction of any tables, and are applicable whether the data are complete or Type II censored. The results have direct application in reliability theory, where the time until the first failure in a group of m items in service provides a measure regarding the operation of the items, as well as in service of fatigue-sensitive aircraft structures to construct strategies of inspections of these structures ; examples of applications are given. Fri, 30 Aug 2024 15:11:10 +0200 Thu, 10 Oct 2024 16:28:03 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=2741 http://popups.lib.uliege.be/1373-5411/index.php?id=2463 In the presented study it is shown how heteroscedastic normal variables with unknown variance can be characterized by a symmetric beta distribution of the first kind with a known parameter. The presented variance-free characterization technique is illustrated with testing for normality the empirically observed financial return time series. We further suggest one of the possible extensions of the presented method that can be used for statistical learning with applications in real-time and time-critical systems. Thu, 22 Aug 2024 10:17:03 +0200 Thu, 22 Aug 2024 10:17:13 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=2463 http://popups.lib.uliege.be/1373-5411/index.php?id=2459 Project portfolio investment is a crucial decision in many organizations, which must make informed decisions on investment, where the appropriate distribution of investment is complex, due to varying levels of risk, resource requirements, and interaction among the proposed projects. In this paper, we discuss an analytical optimal solution to the mean-variance formulation of the problem of optimization of multiperiod investment strategy for project portfolio. Specifically, analytical optimal multiperiod investment strategy for project portfolio is derived. An efficient algorithm is proposed in order to maximize the expected value of the terminal wealth under constraint that the variance of the terminal wealth is not greater than a preassigned risk level or to minimize the variance of the terminal wealth under constraint that the expected terminal wealth is not smaller than a preassigned level. A numerical example is given. Thu, 22 Aug 2024 10:03:16 +0200 Thu, 10 Oct 2024 09:46:52 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=2459 http://popups.lib.uliege.be/1373-5411/index.php?id=2184 A primary application of regression analysis is prediction. In this paper, we consider the definition of the domain of the model in which prediction is valid. This is important because prediction made outside the domain may be unacceptably different from the true responses. We provide a criterion that can be used to decide whether prediction is valid at a certain point. The criterion is based on the existence of an unbiased estimate of the distribution function associated to the "future" observation. In addition, in the context of regression analysis, the categorical control problem that is quite different from the numerical control problem in the setting of the target is considered. Categorical control may be compared to interval prediction, whereas numerical control is compared to point prediction. Our derivation is based on the Scheffé-type simultaneous tolerance interval at two distinct points. Tue, 30 Jul 2024 12:43:28 +0200 Tue, 30 Jul 2024 12:43:35 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=2184 http://popups.lib.uliege.be/1373-5411/index.php?id=2051 In the present paper, for constructing the minimum risk estimators of state of stochastic systems, a new technique of invariant embedding of sample statistics in a loss function is proposed. This technique represents a simple and computationally attractive statistical method based on the constructive use of the invariance principle in mathematical statistics. Unlike the Bayesian approach, an invariant embedding technique is independent of the choice of priors. It allows one to eliminate unknown parameters from the problem and to find the best invariant estimator, which has smaller risk than any of the well-known estimators. Also the problem of how to select the total number of the observations optimally when a constant cost is incurred for each observation taken is discussed. To illustrate the proposed technique, an example is given. Fri, 26 Jul 2024 16:07:39 +0200 Fri, 26 Jul 2024 16:07:49 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=2051 http://popups.lib.uliege.be/1373-5411/index.php?id=1980 In the present paper, for optimization of interval estimators, a new technique of invariant embedding of sample statistics in a loss function is proposed. This technique represents a simple and computationally attractive statistical method based on the constructive use of the invariance principle in mathematical statistics. Unlike the Bayesian approach, an invariant embedding technique is independent of the choice of priors. The aim of the paper is to show how the invariance principle may be employed in the particular case of finding the interval estimators that are uniformly best invariant. The technique proposed here is a special case of more general considerations applicable whenever the statistical problem is invariant under a group of transformations, which acts transitively on the parameter space. This technique may be used for constructing the minimum risk estimators of state of computing anticipatory systems. To illustrate the proposed technique, examples are given. Fri, 19 Jul 2024 09:08:39 +0200 Fri, 19 Jul 2024 09:08:49 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=1980 http://popups.lib.uliege.be/1373-5411/index.php?id=925 This paper deals with the stochastic adaptive linear quadratic optimal control problems which have been an active area of research for many years. It has been known that these problems could be treated by dynamic programming. However, it has been conceded that explicit solution of the dynamic programming equations for these problems is generally not possible and that numerical solution of these equations is a difficult computational procedure. This has led to many approximation techniques. In the paper, a variational approach is used to obtain optimality conditions for the stochastic linear quadratic adaptive control problems. These conditions lead to an algorithm for computing optimal control laws which differs from the dynamic programming algorithm. If the unknown parameters enter into the state equation additively, and the prior distribution of the unknown parameters is normal, the algorithm can be carried out in closed form. The examples are given to illustrate the proposed technique. Mon, 01 Jul 2024 14:08:23 +0200 Thu, 10 Oct 2024 16:17:00 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=925 http://popups.lib.uliege.be/1373-5411/index.php?id=258 In this paper, the problem of determining the optimal control law for discrete-time stochastic linear systems with respect to a quadratic performance criterion is considered. It is assumed that the system is subject to additive system noise and that the state variables are measured with additive measurement noise, without specifying the specific characteristics of random variables. It is shown that the problem of stochastic optimal control can be reduced to two independent problems, one of equivalent deterministic optimal control and the other of stochastic estimation of underlying uncertainties. This holds even if the system noise, the measurement noise and/or the initial state of the system are non-Gaussian, mutually and time-wise dependent. The aim of the present paper is to show how the invariant embedding technique and fiducial approach may be used to solve the problem of adaptive cautious controlling a discrete-time stochastic linear system in which the state transition matrix and the control driven matrix are unknown. This is the case when the certainty equivalence principle does not yield the admissible adaptive control laws for the present problem. The proposed approach does not require the arbitrary selection of priors as in the Bayesian approach. It makes it possible to simplify the problem of adaptive optimization of stochastic systems and, if the system noise and/or the measurement noise are Gaussian, to carry out the algorithm in closed form. The examples are given to illustate the suggested methodology. Wed, 19 Jun 2024 15:17:36 +0200 Wed, 19 Jun 2024 15:17:46 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=258